I consider symmetry to be one of the most important math concepts that Kindergartners learn. It seems an easy concept to teach, but many children have difficulty grasping the concept. I use pictures of butterflies and have the kids color them in symmetrically and asymmetrically--and in the process--they learn both terms. Here are some steps to teaching symmetry.
Explain to the children that the concept of symmetry means "same on both sides." Show them examples of things that are and are not symmetrical.
Give the students this butterfly to color in. I do not show them an example of a symmetrical butterfly; I want to see which students can grasp the concept without seeing an example.
Give them the second butterfly sheet with two butterflies and ask them to color one of them symmetrically and the other asymmetrically.
Give them one more sheet with four butterflies and ask them to color all of them symmetrically.